You'd shoot at the same aperture and shutter speed, so there's no difference in depth-of-field or motion blur. The camera will say you're underexposing. If you're not using manual mode, you'll have to dial in negative exposure compensation to tell the camera to do that. Image review will also be less useful, since the camera will be showing you the underexposed shots. That's why I said that in practice it may be easier to just let the camera use the higher ISO. Certainly if you're not risking highlight clipping--then there's no downside to letting the camera do the multiplication.

But if you're backed into a corner and think you need f/2, 1/100, ISO 3200, and as much dynamic range as you can get, and if you have time to set everything up, then theoretically you're better off shooting at f/2, 1/100, ISO 800, and then pushing it two stops in the RAW converter. You'll get two more stops of DR for highlight recovery, while your shadows will be no noiser than if you had used ISO 3200 in-camera .